On singular Calogero-Moser spaces

Details On singular Calogero-Moser spaces On singular Calogero-Moser spaces

2007-07-25

arxiv.org/abs/0707.3694v2

Mathematics

Representation Theory

Conjecture 1.3 of version 1 is proved as Corollary 4.2

Scientific paper

Using combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter c if and only if the group is different from the wreath product $S_n\wr C_m$ and the binary tetrahedral group. This result and a theorem of Ginzburg and Kaledin imply that there does not exist a symplectic resolution of the singular symplectic variety h+h*/W outside of these cases; conversely we show that there exists a symplectic resolution for the binary tetrahedral group (Hilbert schemes provide resolutions for the wreath product case).

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